Displacement modifier as a wave?
Another 'In Principle' option...

Animate a 'pulse' mesh along a curve derived from, or used to construct, your blood vessel, using a Curve deform modifier, keying the location of the pulse mesh along its deformation axis:



Give the blood vessel a  Vertex Group for displacement, set to 0. (Vertices outside the group altogether will not be affected) Assign a Vertex Weight Proximity modifier, using the vertex group, targeted on the pulse mesh:



Assign a Displace modifier to the blood vessel, aimed at the vertex group.



'In principle', because, to say the least, you probably want the shape of your deformer, weight influence, timing, everything to be tweaked differently. :D But all the adjustments are available.

The pulse mesh could itself be shape-keyed on its journey, to modulate the expansion.